Chapter 10.1, Problem 15E

To determine

To calculate:

Number for which experimental probability of rolling the number the same as theoretical probability.

Answer to Problem 15E

The probability of the event that the face for comes up in the throwing of die is equal to the theoretical probability f or the particular face coming up.

Explanation of Solution

Given information:

  

Calculation:

The question is related to probability of the favorable event.

Event is considered as throwing a die for a consecutive $60$ times and thus recording the outcomes that are received.

Now, the probability that a given face comes up at random at any throw is given by,

  $P$ (Any face coming up)

  $=\frac{1}{6}$

The outcomes as recording after throwing the die for a consecutive $60$ times is shown in given table.

Now the probabilities for each faces are getting by,

  $P$ ( $1$ coming up)

  $=\frac{11}{60}$

  $P$ ( $2$ coming up)

  $\begin{array}{l}=\frac{14}{60}\\ =\frac{7}{60}\end{array}$

  $P$ ( $3$ coming up)

  $=\frac{7}{60}$

  $P$ ( $4$ coming up)

  $=\frac{10}{60}$

  $P$ ( $5$ coming up)

  $=\frac{6}{60}$

  $P$ ( $6$ coming up)

  $\begin{array}{l}=\frac{12}{60}\\ =\frac{1}{5}\end{array}$

Hence, the probability of the event that the face for comes up in the throwing of die is equal to the theoretical probability for the particular face coming up.